// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_PRODUCT_H
#define EIGEN_PRODUCT_H

namespace Eigen {

template<typename Lhs, typename Rhs, int Option, typename StorageKind>
class ProductImpl;

namespace internal {

template<typename Lhs, typename Rhs, int Option>
struct traits<Product<Lhs, Rhs, Option>>
{
	typedef typename remove_all<Lhs>::type LhsCleaned;
	typedef typename remove_all<Rhs>::type RhsCleaned;
	typedef traits<LhsCleaned> LhsTraits;
	typedef traits<RhsCleaned> RhsTraits;

	typedef MatrixXpr XprKind;

	typedef typename ScalarBinaryOpTraits<typename traits<LhsCleaned>::Scalar,
										  typename traits<RhsCleaned>::Scalar>::ReturnType Scalar;
	typedef typename product_promote_storage_type<typename LhsTraits::StorageKind,
												  typename RhsTraits::StorageKind,
												  internal::product_type<Lhs, Rhs>::ret>::ret StorageKind;
	typedef typename promote_index_type<typename LhsTraits::StorageIndex, typename RhsTraits::StorageIndex>::type
		StorageIndex;

	enum
	{
		RowsAtCompileTime = LhsTraits::RowsAtCompileTime,
		ColsAtCompileTime = RhsTraits::ColsAtCompileTime,
		MaxRowsAtCompileTime = LhsTraits::MaxRowsAtCompileTime,
		MaxColsAtCompileTime = RhsTraits::MaxColsAtCompileTime,

		// FIXME: only needed by GeneralMatrixMatrixTriangular
		InnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(LhsTraits::ColsAtCompileTime, RhsTraits::RowsAtCompileTime),

		// The storage order is somewhat arbitrary here. The correct one will be determined through the evaluator.
		Flags = (MaxRowsAtCompileTime == 1 && MaxColsAtCompileTime != 1)   ? RowMajorBit
				: (MaxColsAtCompileTime == 1 && MaxRowsAtCompileTime != 1) ? 0
				: (((LhsTraits::Flags & NoPreferredStorageOrderBit) && (RhsTraits::Flags & RowMajorBit)) ||
				   ((RhsTraits::Flags & NoPreferredStorageOrderBit) && (LhsTraits::Flags & RowMajorBit)))
					? RowMajorBit
					: NoPreferredStorageOrderBit
	};
};

} // end namespace internal

/** \class Product
 * \ingroup Core_Module
 *
 * \brief Expression of the product of two arbitrary matrices or vectors
 *
 * \tparam _Lhs the type of the left-hand side expression
 * \tparam _Rhs the type of the right-hand side expression
 *
 * This class represents an expression of the product of two arbitrary matrices.
 *
 * The other template parameters are:
 * \tparam Option     can be DefaultProduct, AliasFreeProduct, or LazyProduct
 *
 */
template<typename _Lhs, typename _Rhs, int Option>
class Product
	: public ProductImpl<_Lhs,
						 _Rhs,
						 Option,
						 typename internal::product_promote_storage_type<typename internal::traits<_Lhs>::StorageKind,
																		 typename internal::traits<_Rhs>::StorageKind,
																		 internal::product_type<_Lhs, _Rhs>::ret>::ret>
{
  public:
	typedef _Lhs Lhs;
	typedef _Rhs Rhs;

	typedef typename ProductImpl<
		Lhs,
		Rhs,
		Option,
		typename internal::product_promote_storage_type<typename internal::traits<Lhs>::StorageKind,
														typename internal::traits<Rhs>::StorageKind,
														internal::product_type<Lhs, Rhs>::ret>::ret>::Base Base;
	EIGEN_GENERIC_PUBLIC_INTERFACE(Product)

	typedef typename internal::ref_selector<Lhs>::type LhsNested;
	typedef typename internal::ref_selector<Rhs>::type RhsNested;
	typedef typename internal::remove_all<LhsNested>::type LhsNestedCleaned;
	typedef typename internal::remove_all<RhsNested>::type RhsNestedCleaned;

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Product(const Lhs& lhs, const Rhs& rhs)
		: m_lhs(lhs)
		, m_rhs(rhs)
	{
		eigen_assert(lhs.cols() == rhs.rows() && "invalid matrix product" &&
					 "if you wanted a coeff-wise or a dot product use the respective explicit functions");
	}

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_lhs.rows(); }
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_rhs.cols(); }

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const LhsNestedCleaned& lhs() const { return m_lhs; }
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const RhsNestedCleaned& rhs() const { return m_rhs; }

  protected:
	LhsNested m_lhs;
	RhsNested m_rhs;
};

namespace internal {

template<typename Lhs, typename Rhs, int Option, int ProductTag = internal::product_type<Lhs, Rhs>::ret>
class dense_product_base : public internal::dense_xpr_base<Product<Lhs, Rhs, Option>>::type
{};

/** Conversion to scalar for inner-products */
template<typename Lhs, typename Rhs, int Option>
class dense_product_base<Lhs, Rhs, Option, InnerProduct>
	: public internal::dense_xpr_base<Product<Lhs, Rhs, Option>>::type
{
	typedef Product<Lhs, Rhs, Option> ProductXpr;
	typedef typename internal::dense_xpr_base<ProductXpr>::type Base;

  public:
	using Base::derived;
	typedef typename Base::Scalar Scalar;

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE operator const Scalar() const
	{
		return internal::evaluator<ProductXpr>(derived()).coeff(0, 0);
	}
};

} // namespace internal

// Generic API dispatcher
template<typename Lhs, typename Rhs, int Option, typename StorageKind>
class ProductImpl : public internal::generic_xpr_base<Product<Lhs, Rhs, Option>, MatrixXpr, StorageKind>::type
{
  public:
	typedef typename internal::generic_xpr_base<Product<Lhs, Rhs, Option>, MatrixXpr, StorageKind>::type Base;
};

template<typename Lhs, typename Rhs, int Option>
class ProductImpl<Lhs, Rhs, Option, Dense> : public internal::dense_product_base<Lhs, Rhs, Option>
{
	typedef Product<Lhs, Rhs, Option> Derived;

  public:
	typedef typename internal::dense_product_base<Lhs, Rhs, Option> Base;
	EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
  protected:
	enum
	{
		IsOneByOne = (RowsAtCompileTime == 1 || RowsAtCompileTime == Dynamic) &&
					 (ColsAtCompileTime == 1 || ColsAtCompileTime == Dynamic),
		EnableCoeff = IsOneByOne || Option == LazyProduct
	};

  public:
	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index row, Index col) const
	{
		EIGEN_STATIC_ASSERT(EnableCoeff, THIS_METHOD_IS_ONLY_FOR_INNER_OR_LAZY_PRODUCTS);
		eigen_assert((Option == LazyProduct) || (this->rows() == 1 && this->cols() == 1));

		return internal::evaluator<Derived>(derived()).coeff(row, col);
	}

	EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index i) const
	{
		EIGEN_STATIC_ASSERT(EnableCoeff, THIS_METHOD_IS_ONLY_FOR_INNER_OR_LAZY_PRODUCTS);
		eigen_assert((Option == LazyProduct) || (this->rows() == 1 && this->cols() == 1));

		return internal::evaluator<Derived>(derived()).coeff(i);
	}
};

} // end namespace Eigen

#endif // EIGEN_PRODUCT_H
